An object's two dimensional velocity is given by #v(t) = ( t^2 - 2t , cospit - t )#. What is the object's rate and direction of acceleration at #t=1 #?

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Answer 1 · 2017-05-06T08:35:55

#"answer :"a(1)=(0,-1)#

#d/(d t) v(t)=(color(red)(d/(d t)(t^2-2t)),color(green)(d/(d t)(cos pi t-t)))#

#d/(d t) v(t)=a(t)#

#a(t)=(color(red)(2t-2),color(green)(-pi sin pi t-1))#

#"solve t=1"#

#a(1)=(2*1-2,-pi sin pi *1-1)#

#a(1)=(0,-pi sin pi-1)#

#sin pi=0#

#a(1)=(0,-1)#